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3 years ago

Write the equation of the line with x-intercept 3 and passing through the point (5,4).

Mathematics

1 answer:

STALIN [3.7K]3 years ago

5 0

Answer:

The equation of the line is y = 2x - 6

Step-by-step explanation:

To find the equation of this line, we first need to find the slope. To find a slope you need two ordered pairs, which you have here. The first is (5, 4) and the second is (3, 0) - which is the x-intercept of 3. Now that we have this, we can plug into the slope equation.

m(slope) = (y2 - y1)/(x2 - x1)

m = (4 - 0)/(5 - 3)

m = 4/2

m = 2

Now that we have the slope, we can use that and either point in point-slope form. Once we do that, we solve for y to get the equation.

y - y1 = m(x - x1)

y - 4 = 2(x - 5)

y - 4 = 2x - 10

y = 2x - 6

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Answer:

The function g(x) is defined as $g(x)=-\frac{1}{6}(0.2)^{x-9}$ .

Step-by-step explanation:

The given function is

$f(x)=-(0.2)^x$

The function f(x) transformed 9 units right, compressed vertically by factor of 1/6 and reflected across the x-axis.

The transformation of function is defined as

$g(x)=kf(x+b)+c$

Where, k is vertical stretch, b is horizontal shift and c is vertical shift.

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If c>0, then the graph of f(x) shifts c units upward and if c>0, then the graph of f(x) shifts c units downward.

The value of b is -9 because the graph shifts 9 units right. The value of k is 1/6. If the graph of function f(x)reflect across x-axis, therefore the function is defined as -f(x).

$g(x)=\frac{1}{6}(-f(x-9))$

$g(x)=-\frac{1}{6}(0.2)^{x-9}$ $[\because f(x)=-(0.2)^x]$

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